Graph_Theory_and_Posets

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title: Graph Theory and Posets permalink: wiki/Graph_Theory_and_Posets/ layout: wiki

Much work has been done on this topic at previous workshops. So the first task of this group is to assess the current status of this project. Contacting Sonja Mapes (See MSRI2010 participant listings) would be a good first step. Then determine a plan of action.

Sonja's suggestions

• Fix displayGraph for Hasse diagrams. (couldn't duplicate, but possibly was fixed by the below item)
• Fix displayGraph for graphs with vertices with names longer than one character.
• Fix tests at the end of the Posets code.

Day 1

• Fixed displayGraph bug.
• Incidence/adjacency matrices.

Day 2

• Joined forces with Algebraic Statistics CC2010. Topological sort of digraphs.

Day 3

• Rewrite moebiusFunction code for Posets.
• Fix Poset tests. 3 5 8 11 12 13 14

Day 4

• Presented!
• Continued incidence/adjacency matrices
• Added isCyclic function, used to check that a digraph is indeed a dag before attempting topSort.
• Fixed the rest of the original Posets tests, although now there is a conflict between adjacencyMatrix in Graphs and adjacencyMatrix in Posets.

Day 5

• Added showTikZ function, which uses dot2tex to display TikZ (or pgf) code for a graph.
• Fixed adjacencyMatrix conflicts by moving everything to Graphs (including Floyd-Marshall algorithm)

Questions

• What about hypergraphs, multigraphs, loop graphs, weighted graphs, etc?
• What about EdgeIdeals package?
• Should neighbors/children of each vertex be lists or sets in the hash table? (I think lists so scan/apply can be used, but some methods, e.g., graph(List) and completeGraph(ZZ), spit out sets.)

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